222 



NATURE 



[May 17, 19 1 7 



should hesitate between Clerk Maxwell and 

 H. J. S. Smith. Both are mathematicians of the 

 first rank; both are cultured, witty, and childlike; 

 one has all the virtues of the Irishman, the other 

 all those of the Scot, Smith is the more elegant 

 and careful writer; Maxwell is in closer contact 

 with Nature, and possibly has done more to raise 

 her mysterious veil. But Smith's very aloofness, 

 his fondness for what "has no possible practical 

 application," may only mean that he approached 

 the sanctuary by a different road. Of his mordant 

 wit the lecturer gives various samples; he even 

 has the shameless audacity to quote : " • some- 

 times forgets that he is only the editor, and not 

 the author, of Nature." Smith's practical com- 

 mon sense, shown in dealing with university and 

 college affairs, illustrates the fact that a mathe- 

 matician is not always a nincompoop outside the 

 range of his science. 



Sylvester is one of the many Jews who have 

 distinguished themselves as pure mathematicians. 

 Self-conceited, irritable, careless as he was, he 

 was eminently original, inspiring, and generous. 

 His unbroken friendship with Cayley is no doubt 

 mainly a credit to the latter, but it is very touch- 

 ing ; and although Sylvester was not a model 

 teacher he was stimulating, and had great influ- 

 ence on the best of his hearers. MacFarlane's 

 account of him is, as it should be, both amusing 

 and pathetic; it contains, among other things, 

 Sylvester's brilliant retort to Huxley's deprecia- 

 tion of mathematics ; this was one of the few 

 cases in which Huxley was conclusively refuted. 



The remaining two lectures are in some ways 

 the most valuable of the ten, especially that on 

 Kirkman. We wonder how many of our readers 

 ever heard of Kirkman and his work; yet he 

 was really a very brilliant mathematician, 

 although comparatively unknown — partly from his 

 own fault, partly from that of others. He used 

 to send scores of ingenious problems to the 

 Educational Times (many of them in doggerel 

 verse) ; these would be quite worth looking up. 

 Besides this, he did some very important work 

 on the classification of polyhedra; the result was 

 communicated to the Royal Society, and we are 

 told here (p. 127) that only two of the twenty- 

 one sections were published in the Philosophical 

 Transactions. If this is true, it is little short of 

 a scandal, and the rest of the MS. should be sent 

 to Prof. Burnside, as the subject is closely con- 

 nected with group-theory. We are also informed 

 that there are papers on groups by Kirkman 

 embedded in* the Proceedings of the Manchester 

 Philosophical Society [the R.S. subject index, 

 p. 65, gives references to vols, i., iii., iv. (1862-65) 

 and to vols. iv. , v. of the later series (1891-92)]. 

 Current English text-books on the subject 

 give no reference to Kirkman at all ; yet 

 our lecturer says : " So far as British contributors 

 are concerned, Kirkman was the first and still 

 remains the greatest." Whether this is true or 

 not, the matter requires investigation. 



On p. 132 we have Kirkman 's delightful para- 

 phrase of Spencer's definition of evolution, and 

 NO. 2481, VOL. 99] 



a reference to his work on knots; and on p. 133 

 his neat little problem : — 



Baby Tom of baby Hugh . 



The nephew is and uncle too ; 



In how many ways can this be true? 



which we leave for our readers to solve. The 

 lecture ends with a quotation from one of Kirk- 

 man's letters: "What I have done in helping 

 busy Tait in knots is, like the much more difficult 

 and extensive things I have done in polyhedra or 

 groups, not at [all] likely to be talked about intel- 

 ligently by people so long as I live. But it is a 

 faint pleasure to think it will one day win a little 

 praise." , 



All of us remember Todhunter as a coach and 



the author of text-books which in their time were 



thought the embodiment of perfection and are 



now unduly depreciated. But Todhunter was 



much more than a writer of text-books ; his 



mathematical histories are deservedly accounted 



classics, and in them he was able to display his 



learning, accuracy, and acumen. We are very 



glad that a lecture was devoted to him, and that 



it is so sympathetic. Of course, we have the 



famous passage on experimental science, with its 



doctrine of taking everything on the word of " a 



clergyman of mature knowledge, recognised 



' ability, and blameless character," but we have 



much more than that. Isaac had no ear for 



I music, but he h^d a sort of dry humour of his 



' own, as when he quotes the words of a Tripos 



candidate who was ploughed : " If there had been 



I fairer examiners and better papers I should have 



! passed; I knew many things that were not set." 



! The book ends with a quotation from Prof. 



I (J. E. B. ?) Mayor: "Todhunter had no enemies, 



j for he neither coined nor circulated scandal ; men 



j of all sects and parties were at home with him, 



j for he was many-sided enough to see good in 



everything. His friendship extended even to the 



lower creatures. ■ The canaries always hung in 



his room, for he never forgot to see to their 



wants." May we all have as good an epitaoh ! 



G. B. M. 



THE FRESH-WATER FISHES OF RUSSIA. 

 Les Poissons des Eaux douces de la Russie. Par 

 L.' S. Berg. Pp. xxvii + 563 + 365 text-figures 

 and a map. (Moscow: Department of Agri- 

 culture, 1916.) 

 TDROF. BERG'S work on the fresh-water fishes 

 -■- of the Russian Empire, complete in one 

 volume, will be welcomed by all ichthyologists, 

 for the author's knowledge of Palaearctic fishes 

 is unrivalled. In plan this work is more con- 

 densed than the very elaborate monograph 

 (" Faune de la Russie : Poissons ") on which Prof. 

 Berg was engaged, and of which three parts had 

 already app>eared, when in 191 4 he gave up the 

 •curatorship'of fishes in the Imperial Academy of 

 Sciences at Petrograd to become the first professor 

 of ichthyology in the Academy of Agriculture at 

 Moscow. 



The book is written entirely in Russian, and 



